I want to implement a not so slow function for counting/generating all
placements of non-attacking rooks in a board. Currently I am generating all
partial permutations and checking whether they are in the board.
An alternative would be to encode the board belonging to an n x n grid as a
On 2013-03-19, Victor Miller victorsmil...@gmail.com wrote:
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Suppose that A is an m by n integer matrix. Its Gram matrix is G = A*A^t.
If A is not full rank, then G has some eigenvalues of 0. If I do
Thanks Dima and John, In the meantime, since I have Magma available to me I
tried to use magma's functions. What I'm really interested is getting the
unimodular (when it makes sense to use that term) transition matrix needed
to put a matrix in reduced form. It looks like, but correct me if
Aha, I found the nvals= option to magma commands. So for now I'll use
that. I would like to ask that LLL optionally return the transition matrix
(and also BKZ if that's possible).
Victor
On Tuesday, March 19, 2013 2:38:02 PM UTC-4, Victor Miller wrote:
Suppose that A is an m by n integer
I found the matching_polynomial
http://www.sagemath.org/doc/reference/graphs/sage/graphs/matchpoly.html#sage.graphs.matchpoly.matching_polynomial
On Wednesday, March 20, 2013 11:17:37 AM UTC-4, Alejandro Morales wrote:
I want to implement a not so slow function for counting/generating all
I use the following to iterate over all matchings and perfect matchings.
def matchings(G):
edges = G.edges(labels = False)
verts = [[v] for v in G]
m = len(edges)
for match in DLXCPP(edges+verts):
yield [edges[t] for t in match if t m]
def perfect_matchings(G):
edges
Note that that code only works for graphs whose vertices are labeled [0...n].
On Wed, Mar 20, 2013 at 1:03 PM, Tom Boothby tomas.boot...@gmail.com wrote:
I use the following to iterate over all matchings and perfect matchings.
def matchings(G):
edges = G.edges(labels = False)
verts =
H... If you want to enumerate all partial permutations then you have
much better to do. If you have a n x m matrix with nm what you should do
it take all subsets of n elements of n, and enumerate all permutations
using those n columns among m. Even if I would LOVE to have a way to
I'm sure it's not fast, but in the file
devel/sage/sage/homology/examples.py, there is a function matching which
gets used in simplicial_complexes.ChessboardComplex(...).
Well, obviously there is a matching function in the Graph class. But
nothing to enumerate them.
Oh. Now that I think of
Thank you very much for all the suggestions. A little bit more of
background. I am working on this patch
http://trac.sagemath.org/sage_trac/ticket/14127
and would like to have an efficient way of generating the rook placements.
On Wednesday, March 20, 2013 11:17:37 AM UTC-4, Alejandro Morales
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